Survey respondents are asked to flip a coin in private and answer
question A if the result is a head and question B if the result is a
tail... what's the probability that Question A will be answered "Yes"?

Suppose you randomly place 2 points on the circumference of a circle.
What is the probability that a 3rd point placed randomly on the circle's
circumference will form a triangle that will contain the center of the
circle?

In a box there are nine fair coins and one two-headed coin. One coin
is chosen at random and tossed twice. Given that heads show both
times, what is the probability that the coin is the two-headed one?
What if it comes up heads for three tosses in a row?

Wandelina has six identical pieces of string held firmly in her fist,
with one end of each sticking out above her fist, and the other end of
each sticking out below her fist. Different people come along and tie the
ends above her hand together, and tie the ends below her hand together.
When Wandelina opens her fist and looks at the strings, what combinations
of different size loops might there be? What is the probability of each
possible combination occurring?

An interesting conversation that defines the general concepts of
average and central tendency, and looks at the usefulness of such
measures both in representing the data and for making predictions
about future events.